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Best diameter for round hole upper entrances?

I'm thinking of using some upper drilled holes as the only entrance to some nuc-type starter colonies in regular hive boxes (with SBB for added ventilation).

I know lots of people advise drilling 3/4" round holes for upper hive body entrances, which can be plugged and opened according to need, with either corks or slider doors.....but
3/4" seems to me to be really large and may be hard for nucs to defend against robbing. Do others use smaller 'corking hole entrances' to advantage? How big do these holes really need to be to allow a good number of bees to go in and out as a main entrance without a huge area to guard against robbing?
Did folks arrive at 3/4" for some particular reason?
Thanks for any thoughts on this.

The little bee returns with evening's gloom,
To join her comrades in the braided hive... -Tennyson